On 19 Feb 2010, at 12:12, Daniel Fischer wrote:
...As far as I know, the term "ring" (in the mathematical sense)
first
appears in chapter 9 - Die Zahlringe des Körpers - of Hilbert's "Die
Theorie der algebraischen Zahlkörper". Unfortunately, Hilbert gives
no hint
why he chose that name (Dedekind, who coined the term "Körper",
called
these structures "Ordnung" [order]).
The Wikipedia article "Ring" says he used it for a specific one where
the elements somehow cycled back.
Yes. And I deem a) the english wikipedia a more reliable source of
information [concerning things mathematical] than the german, b)
Harvey
Cohn more trustworthy than either wikipedia. But a quick look at
Hilbert's
paper didn't reveal the property Cohn mentioned (according to wp)
and no
explanation of Hilbert why he chose the term. So I remain in doubt.
The term "group" was introduced Évariste Galois, though he meant what
we call a cancellative monoid, but since they are finite, have inverses.
So perhaps Hilbert made play on that word: a group is a small number
of people, a ring larger, like a gang.
Hans
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